In general I've come to prefer smaller sized glassware for most cocktails. The total amount of liquid in most of your basic cocktails is usually only about 3 to 4 ounces. Add in a large ice cube and you fill up a standard 6-10 ounce old fashioned glass quite nicely, but it ends up looking lost in a 12-16 ounce double old fashioned glass. This is especially true of a cocktail like the martini or sazerac that is served without ice. A drink that needs more than 8 to 10 ounces should probably be in a collins or highball glass.
Shaken or stirred, that is the question. A while back I took a short "Cocktails 101" class. This was not a bartending class by an means, but rather an introduction to making cocktails. One of the guidelines they offered was when to stir and when to shake. Liquor or spirit based cocktails like the martini and manhattan should be stirred, not shaken (James Bond notwithstanding). Cocktails with fruit juices, dairy, or egg should be shaken and (usually) strained.
For ice that's going in glass, I like to use the Tovolo King Cube ice trays. They make 2 inch cubes that just barely fit in my old fashioned glasses, perfect. I haven't used them myself, but Tovolo also makes a larger tray that makes 1½ inch cubes which sounds like a good size for the shaker. Most ice you get from the average home ice cube tray or ice maker is, in my opinion, just too small. It may start out cold, but you end up very quickly with a diluted, watery drink.
For the longest time I just didn't understand bitters. I've since found that they can add another whole dimension to cocktails and mixed drinks. One reason for this epiphany is the explosion of new and rediscovered bitters. While there is absolutely nothing wrong with Angostura, it's good to know that there is now a growing number of alternative bitters that can add a new twist to an old cocktail (pun intended).
Here's a list of some of my current favorites:
Peychaud's Bitters
Dr Adam Elmegirab's Boker's Bitters
Scrappy's Aromatic Bitters
Fee Brothers Whiskey-Barrel Aged Bitters
Regan's Orange Bitters No. 6
Urban Moonshine Citrus Bitters
Brooklyn Hemispherical Rhubarb Bitters
Bittermens Xocolatl Mole Bitters